A Method for the Identification of Mechanical Properties ...ijcte.org/papers/868-F032.pdfsampling. OLH employs the column pair wise (CP) algorithm [7] and generates an optimal design

Abstract—Identification of material properties involves

physical experimentation followed by modeling, simulation and

manual optimization. However, the last step tends to be

computational expensive. This paper investigates an artificial

neural network (ANN) surrogate model for identifying material

parameters. The proposed approach is illustrated with a case

study based on a nano-indentation test.

Index Terms—Surrogate models, optimization,

metal-mechanic properties, infill sampling, inverse analysis.

I. INTRODUCTION

In material science and engineering, the estimation of

material properties is associated to several applications

including the detection of material failures, and the design of

new materials. Identification of the “strongly-affecting

materials characteristics” is certainly a key for improving the

material design process [1].

Typically, the identification of material properties involves

physical experimentation followed by modeling, simulation

and manual optimization. In the manual optimization step,

different sets of parameter values are proposed and

simulations are performed. The optimization consists in

determining which parameter combination matches best the

physical experimentation data.

This paper focuses on the estimation of material

parameters so that a further identification can be done quicker

and cheaper than with conventional methods.

One conventional technique for estimating mechanical

properties is to approximate a physical responseby means of a

finite element analysis (FEA) model. Firstly, an experiment

is carried out to obtain the physical response. Subsequently,

the FEA model is executed several times in an attempt to

reproduce the physical response. For each model execution,

trial values are assigned to the model input variables (or

parameters), then the model response is compared against the

physical response (see Fig. 1). This method has been reported

for the nanoindentation test [2], in which the problem

consists on finding a FEA prediction that best fits the original

experimental load-depth curve (see Fig. 2).

Although this methodology has proven to be effective in

many cases, its success is highly influenced by the

Manuscript received November 5, 2013; revised January 14, 2014.

Gutierrez L., Li H. Kobayashi M., and Batres R. are with the Department

of Mechanical Engineering, Toyohashi University of Technology,

Toyohashi, Aichi 441-8580, Japan (e-mail: {Leonardo, lihan, m-kobayashi}

@ise.me.tut.ac.jp).

Toda H. is with the Department of Mechanical Engineering, Kyushu

University, Fukuoka 819-0395, Japan (e-mail: [email protected]).

Kuwazuru O. is with the Department of Nuclear Power & Energy Safety,

University of Fukui, Fukui 910-8507, Japan (e-mail: [email protected]).

availability of design experience. Furthermore, it is

impractical when the number of parameters increases, since a

larger number of simulations become necessary.

Fig. 1. Inputs and outputs for an experiment-simulation approach method.

𝑥𝑒𝑥𝑝 and 𝑥𝑠𝑖𝑚 are inputs, 𝑦𝑒𝑥𝑝 and 𝑦 𝑖 are outputs and 𝒑 𝑖 is a trial vector of

parameters.

Fig. 2. Load-depth curve of a nano-indentation experiment and simulations

of trial parameters (. FEA 01, FEA 04).

The proposed approach aims at carrying out as less

simulation runs as possible which are used to generate a

surrogate model that can be utilized “in lieu of the original

computer model” to generate a response with less

computation time. Thus, the surrogate model response can be

compared against the experimental data and optimization

techniques can be employed to find the desired values of the

parameters. Surrogate models are constructed using data

drawn from high-fidelity models, and provide fast

approximations of the objectives and constraints at new

design points, thereby making optimization studies feasible

[3].Common surrogate modeling techniques include splines,

polynomial approximation, Kriging models, radial basis

functions, and artificial neural networks (ANNs).

Simpson et al. (2008) explain the growing usage of

surrogate models [4]. Their review includes many

developments in design and analysis of computer

experiments (DACE) and new surrogate-modeling

techniques proposed during recent decades. On the other

hand, robust methodologies have been developed for

calculating metal-mechanical properties [2]. However, very

few attempts, such in [5], focused on computationally

A Method for the Identification of Mechanical Properties

Using Surrogate Models

Leonardo Gutierrez, Han Li, Hiroyuki Toda, Masakazu Kobayashi, Osamu Kuwazuru, and Rafael Batres

International Journal of Computer Theory and Engineering, Vol. 6, No. 3, June 2014

234DOI: 10.7763/IJCTE.2014.V6.868

efficient methods. Furthermore, most of the existing

literature concentrates in the physical interpretation of the

results, and little has been done on approaches based on

DACE.

Consequently, the objective of this research is to develop a

systematic, general and robust methodology for determining

material parameters within a minimum number of computer

simulations, thus to lower the computational cost of

conventional identification processes.

The rest of this paper is organized as follows. Section II

describes the problem statement. The methodology is

presented in Section III. Section IV illustrates the proposed

approach with a case study for ananoindentation problem.

Finally, the last section draws conclusions and areas of

further research.

II. PROBLEM STATEMENT

The general problem can be stated as follows:

Min 𝑭 𝑥, 𝒑 𝑑𝑥 −𝑥𝑓𝑖𝑛𝑎𝑙

𝑥0

𝑭 𝑥, 𝒑 𝑑𝑥𝑥𝑓𝑖𝑛𝑎𝑙

𝑥0

(1)

subject to 𝑔 𝑥, 𝒑 = 0

where 𝑭 𝑥, 𝒑 is the experiment response, and 𝑭 𝑥, 𝒑 is a

prediction obtained by a surrogate model.

𝑥 is aknown independent variable, 𝒑 is a vector of

parameters which are intrinsically present in the material but

whose range and values are unknown. In contrast, 𝒑 is a

vector of parameters whose values are known a priori. 𝑥0 is

the initial value of 𝑥 , and 𝑥𝑓𝑖𝑛𝑎𝑙 is its last value. The

restriction 𝑔 𝑥, 𝒑 guarantees that the experimental and

predicted responses overlap.

III. METHODOLOGY

Fig. 3. Flowchart of a surrogate-based approach methodology with

embedded ISC.

The methodology follows the super EGO algorithm

proposed by Sasena et al. [6] which guarantees the creation of

an accurate surrogate model. The algorithm works by first

obtaining a set of sample points. Subsequently, rigorous

simulations are performed for each sample point, and a

surrogate model is fitted to those simulation results. The next

step is to optimize the objective function of interest. If a

termination criterion based on infill sampling criterion (ISC)

is not satisfied, then the surrogate model is updated with the

new sample points. Later the ISC is maximized to select the

next sample points to be added. Lastly, the procedure is

repeated until the termination criterion is reached. A

flowchart of this methodology is shown in Fig. 3.

A. Initial Data Sampling Strategy

A finite number of sample points are needed to create a

surrogate model. These points must be well-distributed in the

design space.

In order to ensure the accuracy of the surrogate model in

every region of the design space, various sampling

techniques have been proposed. In this paper, we use the

Latin hypercube sampling (LHS).

A variation of LHS is the optimum Latin hypercube (OLH)

sampling. OLH employs the column pair wise (CP) algorithm

[7] and generates an optimal design with respect to the

S-optimality criterion. S-optimality seeks to maximize the

mean distance from each design point to all the other points in

the design, so the points are as spread out as possible along

the design space.

B. Creation of the Surrogate Model

This step consists of performing simulations at the

designed sampling points. Then the simulation responses are

used for creating the surrogate model. A subsequent

validation process based on a Bayesian metric can be used in

order to decrease the natural uncertainty in surrogate models

with limited number of design points [8].

In this paper we use ANNs as a surrogate method. Some of

the advantages of ANNs are their versatility and simplicity.

ANNs also provide better recognition of patterns in data and

can result in better predictions of the response variables than

conventional methods [9].

ANNs are computational models inspired by animal

central nervous systems (in particular the brain) that are

capable of machine learning and pattern recognition. They

are usually presented as systems of interconnected "neurons"

that can compute values from inputs by feeding information

through the network. Three typical ANNs are back

propagation, conjugate gradient, and Levemberg-Marquardt

methods.

An ANN is trained by repeatedly presenting a series of

input and output pattern sets to the network. The neural

network gradually “learns” the relationship of interest by

modifying the weights between its neurons to minimize the

error between the actual and predicted output patterns of the

training set. Then, a separate set of data called the test set is

used to monitor network‟s performance. During training, the

learning rule is used to iteratively adjust the weights and

biases of the network in order to move the network outputs

closer to the target values by minimizing the network

performance indicator.

If many ANNs are trained, it becomes necessary to choose

the best one by measuring their individual performance. The

ability of surrogate models to reproduce the original model is

commonly quantified by means of metrics such as the

root-mean squared deviation (RMSD).The work in [8] and

[9] shows that aBayesian metric can also be successfully

applied to quantify the probability of data uncertainty in the

prediction done by a set of surrogate models. Shi [8]

employed the RMSD with lnQ Bayesian metric, and Noble

Generate

initial set of

sample points

Run rigorous

simulator

Select the next

sampling point

(ISC)

Stop?

No

Yes

Update set of

sample points

Start

End

Create

surrogate

model

Optimize objective

function of interest


235

[9] employed the Corrected Akaike‟s Information Criterion

(AICc) and the Schwarz‟s Bayesian Criterion (SBC). A

surrogate model is selected in terms of the smallest

uncertainty (in the case of lnQ-metric), or the lowest score (in

the case of AICc and SBC).

C. Optimization with Infill Sampling Criterion

In order to improve the accuracy of the surrogate model

and to facilitate the search of the global optimum, an

approach using Infill Sampling Criterion (ISC) is proposed.

The purpose of ISC is to find the set of parameter values𝒑 𝑖 ,

also called design variable, which maximizes the estimated

error of the surrogate model predictor. Consequently, ISC

searches for areas in the DS with high estimated error. To do

this, ISC uses information of the current model in order to

assess the utility of evaluating a design variable on the actual

problem. The scope of infill criteria ranges from increasing

the global accuracy of the surrogate model to facilitating the

final optimization process.

An example of an ISC-based algorithm for Kriging

surrogate models is the superEGO algorithm introduced by

Sasena et al. [6]. Similar to superEGO, a proposed ISC

approach is done for ANN.

The proposed ISC is based on the offset (error) value

𝐼𝐹 𝒑 , which is a quality index built upon the root mean

squared deviation (RMSD) between the actual response and

simulation data. It can be formulated as

𝐼𝐹 𝒑 = 1

𝑚 𝑭 𝑥𝑖, 𝒑 − 𝑭 𝑥𝑖, 𝒑

2𝑚𝑖=1 ,

(2)

where 𝑭 𝑥𝑖, 𝒑 is the ith actual experiment response at points

𝑥𝑖 , and 𝑭 𝑥𝑖 , 𝒑 is the surrogated prediction at this point, 𝑚 is

the total number of experiment points.

We try to select a parameter design with the biggest

contribution to the current error. In order to estimate the

representativeness of a selected set 𝒑 𝒊 , we introduce a

weighted function

𝑤𝑖 ,𝑗 = 𝑑 𝒑 𝑖 , 𝒑 𝑗 , (3)

where 𝒑 𝑗 is the original OLH sampled data and

𝑑 𝒑 𝑖 , 𝒑 𝑗 = 1 − exp − 𝒑 𝑖 − 𝒑 𝑗 2 . (4)

This weight function gives the similarity of the design

variables. When the two design variables are near each other,

the value of this function is small, and vice versa, the two

design variables are far away, the value is big.

Since this criterion aims to maximize the difference of the

experiment response and those infill variable designs that

significantly deviate from the original OLH sampled data, the

expression of the ISC becomes

𝒑 𝑖 = argmax𝒑 𝑖∈𝐷𝑆 𝑤𝑗 I 𝒑 𝑖 − I 𝒑 𝑗 𝑛𝑗 =1 . (5)

IV. CASE STUDY

The experiment data is given by a nonlinear stress-strain

relationship (hardening curve) in an aluminum-alloy material,

which is obtained by means of a nanoindentation tester.

The nanoindentation experiment is carried out based on

ISO14577-1 (2002) [10]. The experimental response is

shown in Fig.4. The objective is to estimate the values of the

elements of the vector of parameters

𝒑 = 𝐸, 𝐶, 𝑛, 𝛼 . (6)

where 𝐸 is the Young‟s modulus, 𝐶is the the strain-hardening

coefficient, 𝑛 is the strain-hardening exponent and 𝛼 is a

strain constant. The determination of these parameters are

often used to assess the mechanical reliability of materials

(e.g. fatigue, fracture, corrosion and wear) [5], [11], [12].

Fig. 4. Load-depth diagram for the case study indentation problem.𝑥𝑓 : the

final depth of the contact impression after unloading; 𝑦𝑚𝑎𝑥 : the peak

indentation load; 𝑥𝑚𝑎𝑥 : the indenter ideal displacement at peak load; and 𝑘:

the post-experimental calibration.

The nanoindentation test is an extremely small-scale test

carried out with nanometer order displacements, so the

indenter tip is difficult to position exactly over the material

surface at the beginning of the experiment. Hence, the

indenter starts to move downward from above the material

with some gap between the indenter tip and the surface.

When the load cell senses the reaction force from the material

surface, the displacement is set to zero and the force and

displacement start to be recorded. However, the load signal

includes some noise and the digital resolution of load is

restricted, so it is difficult to sense exactly the touching force,

and a delay may also occur. Moreover, the shape of the

indenter tip is not guaranteed to be sharp enough, because the

tip may become rounded by repeated experiments. The

imperfection of the tip shape also affects the error and delay

at the initial contact. Consequently, the indentation

displacement is likely to be underestimated. As a result, the

indentation displacement requires a calibration process that

can correct the initial contact errors.

Here, a calibration factor 𝑘 is introduced as an unknown

constant that represents the difference between an ideal

maximum displacement 𝑥𝑚𝑎𝑥 and the maximum measured

displacement (see Fig. 4).

Since the peak of the indentation load-depth curve is noisy,

the original response is regressed. Then the maximum real

displacement becomes the convergence of a regression of

both the load and the unload curves.

A classic procedure is to adopt a regression using the

power law as suggested by Oliver and Pharr [5], [11]. The

equation of the experimental response, including the

calibration, is restated as


236

𝑭 𝑥, 𝒑 = 𝐴1 𝑥 + 𝐶1 + 𝑘 𝑛1 , 𝑥 ∈ [𝑥0, 𝑥𝑚𝑎𝑥 ]

𝐴2 𝑥 + 𝐶2 + 𝑘 𝑛2 , 𝑥 ∈ [𝑥𝑓 , 𝑥𝑚𝑎𝑥 ]

(7)

where 𝐴𝑖 , 𝐶𝑖 and 𝑛𝑖 are the coefficients of the 𝑖𝑡𝑕 curve

regression, 𝑥 is the depth and 𝑘is the calibration constant of

the whole experimental response.

Since the maximum real displacement is considered to be

the intersection of the loading with the unloading regressed

curves, the value of 𝑘 can be calculated with the least squares

method (LS) using a general purpose optimizer. This

intermediate problem consists in solving

𝑘 = 𝑥𝑚𝑎𝑥 − min𝑥 𝐴1 𝑥 − 𝐶1 𝑛1 − 𝐴2 𝑥 − 𝐶2

𝑛2 , (8)

where the subscript 1 refers to the coefficients that belongs to

the loading regression and 2 refers to the unloading

regression.

A. Sampling Strategy

Because OHS is intended for box-like domains, a

minimum and a maximum limits for each of the sought

parameters must be specified. These upper and lower limits

constitute fixed region in the design space. The parameter

limits are shown in Table I.

TABLE I: DESIGN SPACE OF INPUT VARIABLES

Parameters 𝐸(GPa) 𝐶(MPa) 𝑛 𝑎 Lower Limit 50 500 0.1 0

Upper Limit 150 1500 0.3 0.002

In order to simplify the problem, in this case study we

assume that the set of sample points satisfies the infill

sampling criterion described in Section III.

TABLE II: LHS OF 8 PARTITIONS, 4 VARIABLES

Parameters 𝐸(GPa) 𝐶(MPa) 𝑛 𝑎

1 55.31471 611.9684 0.218075 5.24E-04

2 132.059 549.7711 0.163307 7.85E-04

3 75.79828 715.9358 0.143577 1.94E-03

4 89.83298 848.659 0.108379 4.97E-04

5 119.3931 656.3377 0.265272 1.52E-03

6 144.2803 923.2771 0.198678 1.21E-03

7 108.1492 769.9889 0.291477 1.00E-07

8 69.99183 947.56 0.225471 1.35E-03

Fig. 5. Indenter (yellow), and Aluminum material (blue) in the FEM in 2D

through interface in MARC MENTAT®. Colors represent the scalar

deformation in the contour of the mesh.

The design of experiments was performed using optimum

LHS included in the „LHS‟ package of „R‟ statistical

programming environment. The generated set of sampling

points is shown in Table II.

Subsequently, simulations were carried out on those points

using MARC® simulation software [13]. The numerical data

from the FEA is used for training and verification of the ANN

(see Fig. 5).

B. Creation of the Surrogate Model

In this research, six parameters are considered as input

variables. Four of them represent the material properties, one

is the independent variable (displacement) of the experiment

and one more variable 𝑏 is a binary artifice that helps to

separate the prediction into two sections(load and

unload).For computational purposes, the surrogate model

restated function is

𝑭 𝑥, 𝒑 ≡ 𝑭 𝑥, 𝑏, 𝒑 . (9)

In (9), 𝑏 = 0 represents the loading section of the curve

and 𝑏 = 1 is for the unload section of the curve of Fig. 3.

ANNs were created using the Neuroet toolbox [9]. The

optimum number of neurons in the hidden layer is obtained

via a built-in function in Neuroet.

Additionally, in order to select an adequate surrogate

model, a statistical analysis based on the SBC score was

carried out. The criterion consisted in selecting the ANN

features which have the highest probability of being included

in the top 5% among 3 × 15 × 18 × 12 ANNs‟ SBC scores1.

The analysis showed that for the nano-indentation

response (the load-depth curve), an ANN trained with 8

hidden layers using the standard back-propagation method

produced the smallest SBC. Furthermore, the transfer

function between the input layer and the hidden layer was set

to log-sigmoid, while the transfer function between the

hidden layer and the output layer was pure-linear.

C. Restatement of the Objective Function

In the objective function, it is important to consider that the

experiment is noisy and also could miss certain information

or cluster information in determined sections of the curve.

The first term in (1) that refers to the integration of the

experimental curve is approximated through the integration

of (7) as follows

𝑭 𝑥, 𝑏, 𝒑 𝑑𝑥𝑢𝑓𝑖𝑛𝑎𝑙

𝑢0

≈ 𝐴1 𝑥 + 𝐶1 𝑛1𝑑𝑥𝑥 𝑚𝑎𝑥

𝑥0

+ 𝐴2 𝑥 + 𝐶2 𝑛2𝑑𝑥𝑥 𝑓

𝑥 𝑚𝑎𝑥

(10)

where the coefficients 𝐴1,𝐶1and 𝑛1 belong to a regression of

the load curve and coefficients 𝐴2 ,𝐶2and 𝑛2 belong to the

unload curve.𝑥𝑚𝑎𝑥 is the maximum depth (Fig. 1).

The second term of (1) is approximated as

𝑭 𝑥, 𝒑 𝑑𝑥𝑥𝑓𝑖𝑛𝑎𝑙

𝑥0

≈ 𝑥𝑖 − 𝑥𝑖−1 ∗ 𝑦 𝑖 + 𝑦 1−1

2

𝑛

𝑖=0

(11)

1 In the analysis we compared 3 training methods (Standard

Backpropagation, Conjugate Gradient, and LevembergMarqardt), a best

selection among 15 trainings for each of the 18 candidates for number of

hidden layers (1 to 18), and a final of 12 runs of the whole process selection.


237

where 𝑦 𝑖 is the surrogate model prediction in 𝑥𝑖 .

Finally, the restriction 𝑔 𝑥 is implemented as a composed

penalty function:

𝑔 𝑢 = 𝜔1 ∗ 𝐴1 𝑥𝑚𝑎𝑥 + 𝐶1 𝑛1 − 𝑭 𝑥𝑚𝑎𝑥 , 0, 𝒑 (12)

where 𝜔1is a weight which can be adjusted manually, the

term 𝐴1 𝑥𝑚𝑎𝑥 + 𝐶1 𝑛1 is the peak of the regressed loading

curve, and the term 𝑭 𝑥𝑚𝑎𝑥 , 0, 𝒑 stands for the peak of the

surrogate model loading curve.

The constraint represents a weighted difference between

both the experimental curve and predicted curve peaks. The

value of 𝜔1 is likely to vary depending on the scale of the

prediction, or number of parameters (other features, such as

the dispersion of the original response, could influence it

too). The weight𝜔1 gave satisfactory results for this case

study (4 parameters with a maximum depth of 𝑥𝑚𝑎𝑥 =250[nm]) for the range 0.1 ≤ 𝜔2 ≤ 0.3.

D. Optimization

In the proposed methodology, the purpose is to

strategically find a combination of inputs which solves (1).

Several stochastic optimization algorithms can be used. Since

(1) is a non-linear function, a global optimizer can address

this problem. We used differential evolution algorithm (DE),

[14] to find the optimum material parameters.

E. Results

The calculations were carried out with R, on a Core 2 Duo

computer, running Windows 7 32bits. The optimization was

run 10 times and it took almost 4 minto complete each one.

The results are shown in Table III. Additionally, in order to

validate these results, we compared them to a manually

adjusted FEA procedure based on [2].

TABLE III: RESULTS OBTAINED WITH ANN VS A MANUAL FITTING

Parameters 𝐸(GPa) 𝐶(MPa) 𝑛 𝛼 Optimized

(mean) values 82.95 820.9 0.1308 2.680 E-4

Standard deviation 0.07 3.0 0.001 0.296 E-4

Manually fitted

values 80 800 0.1 0.099 E-4

Fig. 6. Load-depth curve of the physical experiment versus a prediction

generated through ANN method.

The conventional manual fitting required from

material-science experts to perform between 10 to 20

simulations, each one taking approximately 30 minutes in

MARC® on a HP Intel Xeon workstation.

Fig. 6 shows two curves: a) the physical experiment and b)

the optimized surrogated prediction. In the ANN, the

optimum had an RMSD = 0.03551 (mN).

Finally, we made two FEM simulations using both the

optimized mean values, and the manually fitted values from

Table III. Fig. 7 shows the FEM simulation using the

proposed methodology prediction. Table IV contains the

actual RMSD of both curves, each one versus the physical

experiment response.

Fig. 7. Load-depth curve of the physical experiment versus a simulation

using the surrogate-based optimum parameters.

TABLE IV: ACCURACY OF ANN VS MANUAL FITTING

Simulated curves RMSD (mN)

Optimized values 0.0535

Manually fitted values 0.1349

V. CONCLUSION

A method was proposed for the identification of

mechanical properties of materials. The results point out that

surrogate models can be used together with an optimization

algorithm to identify material parameters. A case study was

presented for the estimation of material parameters obtained

from a nanoindentation load-depth curve and a small number

of computer simulations. The proposed systematic

methodology improves the computational and time costs, and

also the accuracy of the existing methods.

Further work includes exploring other surrogate-modeling

techniques such as Kriging or Support Vector Machine, and

comparing. Also a changeable design space is worth

considering. Finally, we plan to investigate more complex

problems involving a larger number of material parameters.

ACKNOWLEDGMENT

We thank Professors Yoshiaki Shimizu, Tatsuhiko

Sakaguchi and Vinicius Aguiar for their valuable advice.

The work carried out in this paper was supported by a grant

from the Japan Society for the Promotion of Science under

Grant-in-Aid for Scientific Research S No. 24226015. This

work was financially supported by JSPS KAKENHI Grant

Number 24226015.


238

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Materials Parameters – Part 1: Test method, ISO14577-1, 2002.

[11] W. C. Oliver and G. M. Pharr, “An improved technique for

determining hardness and elastic modulus using load and displacement

sensing indentation experiments,” Journal of Material Research, vol.

7, pp. 1564-1583, 1992.

[12] X. Chen, J. Yan, and A. M. Karlsson, “On the determination of residual

stress and mechanical properties by indentation,” Materials Science

and Engineering A 416, pp. 139-149, 2006.

[13] MSC.MARC Software, MARC user‟s guide. (2008). [Online].

Available: http://simcompanion.mscsoftware.com/infocenter/index

[14] D. Ardia, K. Boudt, P. Carl, K. Mullen, and B. G. Peterson,

“Differential evolution with DEoptim, an application to non-convex

portfolio optimization,” The R journal, vol. 3, no. 1, pp. 27-34, 2011.

Leonardo Gutierrez received his BS in industrial

engineering from the National Polytechnic Institute in

2012. Currently, Leonardo is pursuing his master‟s

degree in mechanical engineering at Toyohashi

University of Technology in Japan. He worked as Jr.

Functional Oracle E-Business Suite Consultant for SIR

Tecnologia S.A., outsourced in Grupo Aeromexico S.A.,

Oracle Mexico S.A., Grupo GEO S.A. and The Solocup

Company Mexico S.A. until 2012. His current research interests include

computer-aided decision making and optimization. Mr. Gutierrez belongs to

the Industrial Systems Engineering Group in Toyohashi University of

Technology.

Han Li received BS degree in mathematics and applied

mathematics from Faculty of Mathematics and Computer

Science in Hubei University in 2007. She received her

Ph.D. degree in the School of Mathematics and Statistics

at Beijing University of Aeronautics and Astronautics.

Her research interests include neural networks, learning

theory and pattern recognition. She now works as a

researcher in the Department of Mechanical Engineering,

Toyohashi University of Technology. Dr. Li belongs to the Industrial

Systems Engineering Group in Toyohashi University of Technology.

Hiroyuki Toda graduated from Kyoto University in

1987, and received his doctor of engineering degree in

1995. He is currently a distinguished professor in

structural materials and a director of the 3D/4D Structural

Materials Research Centre in Kyushu University. His

research interests are 3D/4D image-based analysis and its

application to understand microstructure-properties

relationships in engineering materials.

Masakazu Kobayashi received his bachelor of

engineering degree from the Faculty of Engineering,

Utsunomiya University in 1996, his master of

engineering degree in 1998 and his doctor of engineering

degree in 2001 also from Utsunomiya University, Japan.

His major is development of 3D analysis method for

material microstructure and its application. He worked as

a researcher at Utsunomiya University before moving on

to Toyohashi. He currently works as an associate professor at the Department

of Mechanical Engineering, Toyohashi University of Technology

Osamu Kuwazuru received his Bachelor of Engineering

degree from the Faculty of Engineering, Shibaura

Institute of Technology in 1996, his Master of

Engineering degree in 1998 and his Doctor of

Engineering degree in 2001 from the University of

Tokyo. His research interests include computational solid

mechanics, nonlinear numerical modeling, 4D imaging,

fatigue, corrosion, and micromechanics. He worked as an

assistant professor at Institute of Industrial Science, the University of Tokyo

between 2001 and 2008, and currently works as an associate professor at

University of Fukui since 2008. Dr. Kuwazuru belongs to the Department of

Nuclear Power & Energy Safety Engineering, University of Fukui.

Rafael Batres is an associate professor of industrial and

systems engineering in the Mechanical Engineering

Department at Toyohashi University of Technology.

Hereceived a BS in chemical engineering from the

National University of Mexico (UNAM) and both a MEng

and PhDin process systems engineering from Tokyo

Institute ofTechnology. His research is currently focused

on material and product design, design and simulation of

sustainable systems, systematic methods for ontology development, and

large-scale data management and analytics.


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A Method for the Identification of Mechanical Properties ...ijcte.org/papers/868-F032.pdfsampling. OLH employs the column pair wise (CP) algorithm [7] and generates an optimal design